[6] sin 2B given sec B - 3 cos 2B and & sin >0. In what quadrant does 2B terminate? 7 5 [7] Verify the identity: 2 csc A sin A 1 + cos A + 1 + cos A sin A
Establish the identity. sec - csc = sin e- cos e sec csc Write the left side as a difference of two quotients. sec csc sec @csc @ Cancel the common factors from the previous step. Do not apply any trigonometric identity. 1-0 The expression from the previous step then simplifies to sin 0 - cos using what? O A. Even-Odd Identity O c. Quotient Identity O E. Pythagorean Identity
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y = 2 sin(x+y)cos(x-y)
Simplify the following trigonometric expression tan(a) sec(0) - cos(e) sin(0) csc() seco) 1 + cos(20)
Verify that the equation is an identity. sin x cOS X secx + = sec?x-tan? CSC X Both sides of this identity look similarly complex. To verify the identity, start with the left side and simplify it. Then work with the right side and try to simplify it to the same result. Choose the correct transformations and transform the expression at each step COS X sin x secx CSC X The left-hand side is simplified enough now, so start working...
Find sin(a) and cos(B), tan(a) and cot(B), and sec(a) and cSC(B). a 14 B (a) sin(a) and cos() (b) tan(a) and cot(6) (c) sec(a) and csc()
4 If sin(0) and is in quadrant II , then find 7. (a) cos(0) = (b) tan(O) = (c) sec(0) = (d) csc(0) = (e) cot(0) =
Solve the equation for the interval [0, 2π). tan x + sec x = 1 csc^5x - 4 csc x = 0 sin^2x - cos^2x = 0 sin^2x + sin x = 0
no cal 3. sin 2x 3 4. sec(-210°) 5. 571 sin STE 6. CSC CE)
Identify the equation as either an identity or not. 13) 1 + CSC X = COS X + cotx sec X A) Identity B) Not an identity 14) sin 0 sec 0 = cos o esco A) Not an identity B) Identity sin X_= 2 CSC X 15) + sin x 1 - COS X 1+cOS X A) Identity B) Not an identity